(x^2-4x+4)=(x-2)^2
(7x^2+x-1)/((2x+1)(x-2)^2)=A/(2x+1)+B/(x-2)+C/(x-2)^2=
=(A(x-2)^2+B(2x+1)(x-2)+C(2x+1))/((2x+1)(x-2)^2)=
=(A(x^2-4x+4)+B(2x^2-3x-2)+C(2x+1))/((2x+1)(x-2)^2)=
=(Ax^2-4Ax+4A+2Bx^2-3Bx-2B+2Cx+C)/((2x+1)(x-2)^2)=
=(x^2(A+2B)+x(-4A-3B+2C)+(4A-2B+C))/((2x+1)(x-2)^2)
A+2B=7 => A=7-2B
-4A-3B+2C=1
4A-2B+C=-1
-28+8B-3B+2C=1
28-8B-2B+C=-1
5B+2C=29
-10B+C=-29
5C=29 => C=29/5
B=(29-2C)/5=29/5-58/25=87/25
A=7-2B = 7-174/25=1/25
I=int (7x^2+x-1)/((2x+1)(x-2)^2) dx
I=1/25int dx/(2x+1)+87/25int dx/(x-2)+29/5intdx/(x-2)^2
I=1/50ln|2x+1|+87/25ln|x-2|-29/(5(x-2))+C